Inequalities with exponential weights

Let R = ( - ∞ , ∞ ) and let Q ∈ C 2 : R → R + = [ 0 , ∞ ) be an even function. Then in this paper we consider the infinite–finite range inequality, an estimate for the Christoffel function, and the Markov–Bernstein inequality with the exponential weights w ρ ( x ) = | x | ρ e - Q ( x ) , x ∈ R .